Depends what you mean. Generally, the screen has a glass substrate which is breakable and therefore you need to protect it. A good case with a front cover is essential in my view for this.
If you mean a plastic front sheet you stick over the device screen to protect the screen from scratches, I haven't used any on my Sony or irex and see no need to. I don't tend to touch the Sony and the stylus on the irex doesn't scratch it. Other users may use such a screen but it won't stop the screen from breaking if you drop it etc.

I find this too. Quite apart from the challenge of getting it on there without bubbles, I find my PRS505 screen protector makes it look 'dirty', less clear and almost more reflective (whch was strange as I specifically bought a matt one).

I don't think it's necessary for an e-ink screen. Maybe for the lcd portion on a nook, but not for the e-ink portion. They don't offer any protection from breakage and if you aren't touching it, then you won't need protection from scratches.

I don't know if this would work for e-ink devices, but you can make your own screen protectors by buying thin plastic sheeting at a craft or fabric store (like Michael's). I made some for one of my Palms. They are a pain to cut at just the right length -- my Dad made a template and then cut some out for me. But they were a lot cheaper than the commercial ones.